Uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball
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DOI: 10.1002/mma.10031
Abstract: In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in ℝ3$$ {\mathrm{\mathbb{R}}}^3 $$ . Under suitable conditions, we prove that, for any given positive integer… read more here.
Keywords: nonlinear elliptic; elliptic equations; solutions nonlinear; uniqueness nodal ... See more keywords
Multibump solutions for nonlinear Schrödinger‐Poisson systems
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DOI: 10.1002/mma.6211
Abstract: In this paper, we study the following Schrödinger‐Poisson equations: −ε2Δu+V(x)u+K(x)ϕu=|u|p−2u,x∈R3,−ε2Δϕ=K(x)u2,x∈R3, where p∈(4,6) , ε>0 is a parameter and V and K satisfy the critical frequency conditions. By using variational methods and penalization arguments, we show… read more here.
Keywords: dinger poisson; schr dinger; solutions nonlinear; multibump solutions ... See more keywords
New exact solutions of a nonlinear integrable equation
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DOI: 10.1002/mma.6419
Abstract: Analytic solutions of the partial differential equations are needed to explain many phenomena seen in thermodynamics, aerodynamics, plasma physics, and other fields. In this paper, variational principle is analyzed of the integrable nonlinear Korteweg–de Vries… read more here.
Keywords: integrable equation; new exact; solutions nonlinear; equation ... See more keywords
Criteria for Blow‐Up Phenomena for Solutions to Nonlinear Reaction–Diffusion Equations on Cones
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DOI: 10.1002/mma.70017
Abstract: This paper investigates the global and nonglobal existence of solutions to nonlinear reaction‐diffusion equations with a general nonlinearity and time‐dependent sources defined on cones of Euclidean spaces. More precisely, the purpose of this work is… read more here.
Keywords: solutions nonlinear; diffusion equations; nonlinear reaction; reaction diffusion ... See more keywords
On maximum principles for solutions to nonlinear elliptic ODEs and radial solutions to nonlinear elliptic PDE's via Opial‐type inequalities
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DOI: 10.1002/mma.7055
Abstract: We consider degenerated nonlinear PDE of elliptic type: −div(a(|x|)|∇w(x)|p−2∇w(x))+h|x|,w(x),∇w(x),x|x|=ϕ(w(x)), a.e. in the ball in ℝn . Using the argument based on Opial‐type inequalities, we investigate qualitative properties of their radial solutions, like, for example, the… read more here.
Keywords: radial solutions; solutions nonlinear; type inequalities; opial type ... See more keywords
Existence of Solutions of Nonlinear and Non-local Fractional Boundary Value Problems
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DOI: 10.1007/s00009-019-1388-9
Abstract: In this paper, we establish new results for non-local boundary value problems. In particular, we study a fractional differential equation where the associated integral equation has a kernel that is not bounded above and changes… read more here.
Keywords: existence solutions; boundary value; solutions nonlinear; non local ... See more keywords
Existence of Solutions for Some Nonlinear Elliptic Equations in Musielak Spaces with Only the Log-Hölder Continuity Condition
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DOI: 10.1007/s00009-019-1466-z
Abstract: We study the existence of solutions for some nonlinear elliptic problems with $$L^1$$L1 data in Musielak spaces; we assume that the Musielak function satisfies only the log-Hölder continuity condition. read more here.
Keywords: solutions nonlinear; lder continuity; musielak spaces; nonlinear elliptic ... See more keywords
Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations
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DOI: 10.1007/s10589-020-00230-x
Abstract: In the case of singular (and possibly even nonisolated) solutions of nonlinear equations, while superlinear convergence of the Newton method cannot be guaranteed, local linear convergence from large domains of starting points still holds under… read more here.
Keywords: convergence; newton method; nonlinear equations; solutions nonlinear ... See more keywords
Blowing Up Solutions for Nonlinear Parabolic Systems with Unequal Elliptic Operators
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DOI: 10.1007/s10884-019-09790-x
Abstract: We give sufficient conditions for the boundedness of the blow-up set and no boundary blow-up for type I blowing up solutions to a nonlinear parabolic system with unequal elliptic operators. We introduce a new method… read more here.
Keywords: solutions nonlinear; blowing solutions; parabolic systems; nonlinear parabolic ... See more keywords
On Convergence to Stationary Distributions for Solutions of Nonlinear Fokker–Planck–Kolmogorov Equations
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DOI: 10.1007/s10958-019-04467-8
Abstract: We obtain conditions under which solutions to a nonlinear Fokker–Planck–Kolmogorov equation with the diffusion matrix depending on the solution converge to the stationary solution. read more here.
Keywords: fokker planck; solutions nonlinear; nonlinear fokker; planck kolmogorov ... See more keywords
Asymptotic behavior of solutions of the nonlinear Beltrami equation with the Jacobian
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DOI: 10.1007/s10958-024-07280-0
Abstract: We investigate the asymptotic behavior at infinity of regular homeomorphic solutions of the nonlinear Beltrami equation with the Jacobian on the right-hand side. The sharpness of the above bounds is illustrated by several examples. read more here.
Keywords: solutions nonlinear; equation jacobian; asymptotic behavior; beltrami equation ... See more keywords